9 citations · 39 across the 30 of their papers we have counts for
20 papers · 1 filter
On Normalizers of Parabolic Subgroups of Quaternionic Reflection Groups
Gerhard Roehrle, Johannes Schmitt
By work of Howlett and Muraleedaran--Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate t…
Parabolic Normalizers in Finite Coxeter Groups as Subdirect Products
J. Matthew Douglass, Götz Pfeiffer, Gerhard Roehrle
We revisit the structure of the normalizer of a parabolic subgroup in a finite Coxeter group , originally described by Howlett. Building on Howlett's Lemma, which p…
On good subgroups, Springer maps, and overgroups of distinguished unipotent elements in reductive groups
Michael Bate, Sören Böhm, Benjamin Martin +1
Suppose is a simple algebraic group defined over an algebraically closed field of good characteristic . In 2018 Korhonen showed that if is a connected reductive subgroup…
Edifices: Building-like spaces associated to linear algebraic groups
Michael Bate, Benjamin Martin, Gerhard Roehrle
Given a semisimple linear algebraic -group , one has a spherical building , and one can interpret the geometric realisation of in terms of cochara…
Complete reducibility for Lie subalgebras and semisimplification
Michael Bate, Sören Böhm, Benjamin Martin +2
Let be a connected reductive linear algebraic group over a field . Using ideas from geometric invariant theory, we study the notion of -complete reducibility over for…
A construction of pseudo-reductive groups with non-reduced root system
Michael Bate, Gerhard Röhrle, Damian Sercombe +1
We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type ; these exist only in cha…
Overgroups of regular unipotent elements in reductive groups
Michael Bate, Ben Martin, Gerhard Roehrle
We study reductive subgroups of a reductive linear algebraic group -- possibly non-connected -- such that contains a regular unipotent element of . We show that unde…
Complete reducibility: Variations on a theme of Serre
Maike Gruchot, Alastair Litterick, Gerhard Roehrle
In this note, we unify and extend various concepts in the area of -complete reducibility, where is a reductive algebraic group. By results of Serre and Bate--Martin--Röhrle,…
Accurate Arrangements
Paul Mücksch, Gerhard Roehrle
Let be a Coxeter arrangement of rank . In 1987 Orlik, Solomon and Terao conjectured that for every , the first exponents of -…
On unipotent radicals of pseudo-reductive groups
Michael Bate, Benjamin Martin, Gerhard Roehrle +1
We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of…
Freeness of multi-reflection arrangements via primitive vector fields
Torsten Hoge, Toshiyuki Mano, Gerhard Roehrle +1
In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We fi…
On the coadjoint orbits of maximal unipotent subgroups of reductive groups
Simon M. Goodwin, Peter Mosch, Gerhard Roehrle
Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \u its Lie al…
On inductively free Restrictions of Reflection Arrangements
Nils Amend, Torsten Hoge, Gerhard Roehrle
Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last t…
Spherical subgroups in simple algebraic groups
Friedrich Knop, Gerhard Roehrle
Let be a simple algebraic group. A closed subgroup of is called spherical provided it has a dense orbit on the flag variety of . Reductive spherical subgroups…
Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven
Simon M. Goodwin, Peter Mosch, Gerhard Roehrle
Let G(q) be a finite Chevalley group, where q is a power of a good prime p, and let U(q) be a Sylow p-subgroup of G(q). Then a generalized version of a conjecture of Higman asserts…
Reflection arrangements are hereditarily free
Torsten Hoge, Gerhard Roehrle
Suppose that W is a finite, unitary, reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each su…
On reflection subgroups of finite Coxeter groups
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
Let be a finite Coxeter group. We classify the reflection subgroups of up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection…
The strong Centre Conjecture: an invariant theory approach
Michael Bate, Benjamin Martin, Gerhard Roehrle
The aim of this paper is to describe an approach to a a strengthened form of J. Tits' Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental…
Complete reducibility and separable field extensions
Michael Bate, Benjamin Martin, Gerhard Roehrle
Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility…
Complete Reducibility and Conjugacy classes of tuples in Algebraic Groups and Lie algebras
M. Bate, B. Martin, G. Roehrle +1
Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G^n, the n-fold Cartesian product of G with itself, by sim…